Using the Slimjet browser to convert a Youtube video to MP3 - slimjet.com
Update June 2022 click show more to read:
YouTube has changed its layout and as SlimJet has not been updated yet the download button doesn't active. Looking into it I've found a workaround. Use the 64bit portable edition of slimjet slimjet.com/en/postdl.php?version=win64&type=zip and when on YouTube, disagree with the request YouTube pops up regarding analytics and once in, do not login to YouTube with your account. This looks like it brings back the download button.
Remember the portable edition does not install itself, it runs directly from the folder its saved in, if you want it at hand, just make a shortcut onto your desktop